## Course Description

Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|---|---|---|---|---|

MATHEMATICS I | - | Fall Semester | 3+0 | 3 | 5 |

Course Program |

Prerequisites Courses | |

Recommended Elective Courses |

Language of Course | Turkish |

Course Level | Short Cycle (Associate's Degree) |

Course Type | Required |

Course Coordinator | Lect. Hatice ÇAY |

Name of Lecturer(s) | Lect. Hatice ÇAY |

Assistant(s) | |

Aim | The aim of this course is to explain fundamental math, calculus and linear algebra contents, methods, techniques and show how to use these methods in solving certain types of problems which might possibly be encountered in many branches of science. |

Course Content | This course contains; Real integers; Basic Algebraic Calculus, Intervals, Absolute Value.,Functions: Functions and Their Graphs, Definition of Trigonometric Functions,Limits and Contiunity: Rates of Change and Tangents to Curves, Limit of a Function and Limit Laws, The Sandwich (The Squeeze theorem), The Precise Definition of a Limit, One-sided Limits,Contiunity: Types of Discontiunity, Continuous Functions, The İntermediate Value Theorem, Limits İnvolving İnfinity, Asymptotes of Graphs,Differentiation: Tangents ,Normal Lines , The Derivative at a Point, The Derivate as a Function, Differentiable on an İnterval, Onesided Derivatives, Differentiation Rules, High order Derivatives, The Derivative as a Rate of Change Derivatives of Trigonometric Fnctions, The chain rule ,Applications of derivatives: Extreme Values of Functions, Critical Points, Rolle’s Theorem, The Mean Value Theorem,Monotonic Functions and The First Derivative Test: Increasing Functions and Decrasing Functions, the First Derivative Test for Local Extrema Concavity and Curve Sketching ,Optimization ,Indefinite Integrals, Integration: Area and Estimating with Finite Sums ,Average Value of Nonnegative Continuous Functions, Sigma Notation and Limits of Finite Sums, Riemann Sums ,Definite İntegral, Properties of Definite İntegral ,Area Under the Graph of a Nonnegative Function, Average Value of Continuous Functions,practice. |

Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |

1. Explain and recognize set of real numbers, absolute value and interval. | 12, 16, 6, 9 | A, D, E, G |

2. Explain functions and their graphics. | 12, 16, 6, 9 | A, D, E, G |

3. Calculate and explain derivatives. | 12, 16, 6, 9 | A, D, E, G |

4. Calculate integrals. | 12, 16, 6, 9 | A, D, E, G |

5. Prove the basic theorems about limits. | 12, 16, 6, 9 | A, D, E, G |

Teaching Methods: | 12: Problem Solving Method, 16: Question - Answer Technique, 6: Experiential Learning, 9: Lecture Method |

Assessment Methods: | A: Traditional Written Exam, D: Oral Exam, E: Homework, G: Quiz |

## Course Outline

Order | Subjects | Preliminary Work |
---|---|---|

1 | Real integers; Basic Algebraic Calculus, Intervals, Absolute Value. | |

2 | Functions: Functions and Their Graphs, Definition of Trigonometric Functions | |

3 | Limits and Contiunity: Rates of Change and Tangents to Curves, Limit of a Function and Limit Laws, The Sandwich (The Squeeze theorem), The Precise Definition of a Limit, One-sided Limits | |

4 | Contiunity: Types of Discontiunity, Continuous Functions, The İntermediate Value Theorem, Limits İnvolving İnfinity, Asymptotes of Graphs | |

5 | Differentiation: Tangents ,Normal Lines , The Derivative at a Point, The Derivate as a Function, Differentiable on an İnterval, Onesided Derivatives, Differentiation Rules, High order Derivatives | |

6 | The Derivative as a Rate of Change Derivatives of Trigonometric Fnctions, The chain rule | |

7 | Applications of derivatives: Extreme Values of Functions, Critical Points, Rolle’s Theorem, The Mean Value Theorem | |

8 | Monotonic Functions and The First Derivative Test: Increasing Functions and Decrasing Functions, the First Derivative Test for Local Extrema Concavity and Curve Sketching | |

9 | Optimization | |

10 | Indefinite Integrals, Integration: Area and Estimating with Finite Sums | |

11 | Average Value of Nonnegative Continuous Functions, Sigma Notation and Limits of Finite Sums, Riemann Sums | |

12 | Definite İntegral, Properties of Definite İntegral | |

13 | Area Under the Graph of a Nonnegative Function, Average Value of Continuous Functions | |

14 | practice |

Resources |

1. Thomas' Calculus, 14th Edition, George B. Thomas, Maurice D. Weir, Joel R. Hass, Pearson. 2. Kısa Teori ve Çözümlü Problemlerle Matematik Analiz 1, Dr. Salih Çelik, Birsen Yayınevi 3. Lecture notes |

## Course Contribution to Program Qualifications

Course Contribution to Program Qualifications | |||||||

No | Program Qualification | Contribution Level | |||||

1 | 2 | 3 | 4 | 5 | |||

1 | Offer necessary applications and solution proposals in the field of biomedical device. | ||||||

2 | Define adequate practical, theoretical and technical knowledge in suitable areas in the field of biomedical device. | ||||||

3 | Take responsibility unpredictable alone or in teams to solve complex problems in applications related to the field. | X | |||||

4 | Use theoretical and practical knowledge in the field of biomedical device. | X | |||||

5 | Reach information and survey resources in the field of biotechnologhy and medicine. | ||||||

6 | Perform maintenance and calibration by troubleshooting of biomedical devices. | X | |||||

7 | Has an ability to design and conduct experiments, and interpret the results. | X | |||||

8 | Demonstrate technical application skills in the medical devices. | X | |||||

9 | Be able to recognize and design electric circuit systems. | X | |||||

10 | Follow the developments in the field of biomedical devices, and critically evaluate the knowledge and skills acquired. | X | |||||

11 | Applies quality assurance and standards by obeying occupational health safety rules in the field of biomedical device. | ||||||

12 | By acting in accordance with professional ethics, principles and values, become a model to colleagues and society. | X |

## Assessment Methods

Contribution Level | Absolute Evaluation | |

Rate of Midterm Exam to Success | 40 | |

Rate of Final Exam to Success | 60 | |

Total | 100 |

ECTS / Workload Table | ||||||

Activities | Number of | Duration(Hour) | Total Workload(Hour) | |||

Course Hours | 14 | 3 | 42 | |||

Guided Problem Solving | 14 | 3 | 42 | |||

Resolution of Homework Problems and Submission as a Report | 3 | 10 | 30 | |||

Term Project | 0 | 0 | 0 | |||

Presentation of Project / Seminar | 0 | 0 | 0 | |||

Quiz | 1 | 2 | 2 | |||

Midterm Exam | 1 | 17 | 17 | |||

General Exam | 1 | 17 | 17 | |||

Performance Task, Maintenance Plan | 0 | 0 | 0 | |||

Total Workload(Hour) | 150 | |||||

Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(150/30) | 5 | |||||

ECTS of the course: 30 hours of work is counted as 1 ECTS credit. |

## Detail Informations of the Course

### Course Description

Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|---|---|---|---|---|

MATHEMATICS I | - | Fall Semester | 3+0 | 3 | 5 |

Course Program |

Prerequisites Courses | |

Recommended Elective Courses |

Language of Course | Turkish |

Course Level | Short Cycle (Associate's Degree) |

Course Type | Required |

Course Coordinator | Lect. Hatice ÇAY |

Name of Lecturer(s) | Lect. Hatice ÇAY |

Assistant(s) | |

Aim | The aim of this course is to explain fundamental math, calculus and linear algebra contents, methods, techniques and show how to use these methods in solving certain types of problems which might possibly be encountered in many branches of science. |

Course Content | This course contains; Real integers; Basic Algebraic Calculus, Intervals, Absolute Value.,Functions: Functions and Their Graphs, Definition of Trigonometric Functions,Limits and Contiunity: Rates of Change and Tangents to Curves, Limit of a Function and Limit Laws, The Sandwich (The Squeeze theorem), The Precise Definition of a Limit, One-sided Limits,Contiunity: Types of Discontiunity, Continuous Functions, The İntermediate Value Theorem, Limits İnvolving İnfinity, Asymptotes of Graphs,Differentiation: Tangents ,Normal Lines , The Derivative at a Point, The Derivate as a Function, Differentiable on an İnterval, Onesided Derivatives, Differentiation Rules, High order Derivatives, The Derivative as a Rate of Change Derivatives of Trigonometric Fnctions, The chain rule ,Applications of derivatives: Extreme Values of Functions, Critical Points, Rolle’s Theorem, The Mean Value Theorem,Monotonic Functions and The First Derivative Test: Increasing Functions and Decrasing Functions, the First Derivative Test for Local Extrema Concavity and Curve Sketching ,Optimization ,Indefinite Integrals, Integration: Area and Estimating with Finite Sums ,Average Value of Nonnegative Continuous Functions, Sigma Notation and Limits of Finite Sums, Riemann Sums ,Definite İntegral, Properties of Definite İntegral ,Area Under the Graph of a Nonnegative Function, Average Value of Continuous Functions,practice. |

Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |

1. Explain and recognize set of real numbers, absolute value and interval. | 12, 16, 6, 9 | A, D, E, G |

2. Explain functions and their graphics. | 12, 16, 6, 9 | A, D, E, G |

3. Calculate and explain derivatives. | 12, 16, 6, 9 | A, D, E, G |

4. Calculate integrals. | 12, 16, 6, 9 | A, D, E, G |

5. Prove the basic theorems about limits. | 12, 16, 6, 9 | A, D, E, G |

Teaching Methods: | 12: Problem Solving Method, 16: Question - Answer Technique, 6: Experiential Learning, 9: Lecture Method |

Assessment Methods: | A: Traditional Written Exam, D: Oral Exam, E: Homework, G: Quiz |

### Course Outline

Order | Subjects | Preliminary Work |
---|---|---|

1 | Real integers; Basic Algebraic Calculus, Intervals, Absolute Value. | |

2 | Functions: Functions and Their Graphs, Definition of Trigonometric Functions | |

3 | Limits and Contiunity: Rates of Change and Tangents to Curves, Limit of a Function and Limit Laws, The Sandwich (The Squeeze theorem), The Precise Definition of a Limit, One-sided Limits | |

4 | Contiunity: Types of Discontiunity, Continuous Functions, The İntermediate Value Theorem, Limits İnvolving İnfinity, Asymptotes of Graphs | |

5 | Differentiation: Tangents ,Normal Lines , The Derivative at a Point, The Derivate as a Function, Differentiable on an İnterval, Onesided Derivatives, Differentiation Rules, High order Derivatives | |

6 | The Derivative as a Rate of Change Derivatives of Trigonometric Fnctions, The chain rule | |

7 | Applications of derivatives: Extreme Values of Functions, Critical Points, Rolle’s Theorem, The Mean Value Theorem | |

8 | Monotonic Functions and The First Derivative Test: Increasing Functions and Decrasing Functions, the First Derivative Test for Local Extrema Concavity and Curve Sketching | |

9 | Optimization | |

10 | Indefinite Integrals, Integration: Area and Estimating with Finite Sums | |

11 | Average Value of Nonnegative Continuous Functions, Sigma Notation and Limits of Finite Sums, Riemann Sums | |

12 | Definite İntegral, Properties of Definite İntegral | |

13 | Area Under the Graph of a Nonnegative Function, Average Value of Continuous Functions | |

14 | practice |

Resources |

1. Thomas' Calculus, 14th Edition, George B. Thomas, Maurice D. Weir, Joel R. Hass, Pearson. 2. Kısa Teori ve Çözümlü Problemlerle Matematik Analiz 1, Dr. Salih Çelik, Birsen Yayınevi 3. Lecture notes |

### Course Contribution to Program Qualifications

Course Contribution to Program Qualifications | |||||||

No | Program Qualification | Contribution Level | |||||

1 | 2 | 3 | 4 | 5 | |||

1 | Offer necessary applications and solution proposals in the field of biomedical device. | ||||||

2 | Define adequate practical, theoretical and technical knowledge in suitable areas in the field of biomedical device. | ||||||

3 | Take responsibility unpredictable alone or in teams to solve complex problems in applications related to the field. | X | |||||

4 | Use theoretical and practical knowledge in the field of biomedical device. | X | |||||

5 | Reach information and survey resources in the field of biotechnologhy and medicine. | ||||||

6 | Perform maintenance and calibration by troubleshooting of biomedical devices. | X | |||||

7 | Has an ability to design and conduct experiments, and interpret the results. | X | |||||

8 | Demonstrate technical application skills in the medical devices. | X | |||||

9 | Be able to recognize and design electric circuit systems. | X | |||||

10 | Follow the developments in the field of biomedical devices, and critically evaluate the knowledge and skills acquired. | X | |||||

11 | Applies quality assurance and standards by obeying occupational health safety rules in the field of biomedical device. | ||||||

12 | By acting in accordance with professional ethics, principles and values, become a model to colleagues and society. | X |

### Assessment Methods

Contribution Level | Absolute Evaluation | |

Rate of Midterm Exam to Success | 40 | |

Rate of Final Exam to Success | 60 | |

Total | 100 |